Electronic filter
Electrical and communication equipment described circuits as the filter ( in jargon usually the filter ), change an electric signal dependent on the frequency in the amplitude and in the phase position. This unwanted signal components are markedly attenuated and largely suppressed.
- 5.1 filter and frequency response, selection behavior
- 5.2 Linear and non-linear filter 5.2.1 Linear Filters
- 5.2.2 Non-linear filter
- 5.3.1 Passive filters or electrical filter
- 5.3.2 Active filter or an electronic filter
- 5.3.3 Analog filters
- 5.3.4 Digital filters and digital signal processors (DSP)
- 5.3.5 Other filters
Classification and applications
Filters can be classified according to several criteria, for example, according to their complexity, their frequency response, the components used, the circuit structure of the calculation method used, the selectivity or slope and the phase shift.
Filter in the classical sense, as low or high pass, change the frequency response. They are also known as filter circuits. Circuits and methods that alter the complex properties such as phase angle, impedance and noise components are also summarized under the term filter. The sound digital and analog frequency filter ( filter) as equalizers are ( briefly EQ ) and are used as sound effects. This includes presence, absence, band -pass, high -pass and low -pass filter.
Known applications are:
- Radio / broadcasting: selection of a particular transmission frequency to a station to receive. Only the set frequency is received. All other frequencies are filtered out.
- Speakers ( crossover ): The different frequencies for treble, bass and midrange are split and distributed to the appropriate speakers.
- Filter: They suppress clicks when switching from other consumers and other disruptions
History
The foundations of the theory of electrical filters were developed as early as 1915 by the German Karl Willy Wagner and the American George Ashley Campbell.
Frequency filter
Frequency filters are circuits ( " networks " called ) with a given frequency-dependent transmission characteristics (frequency response ), the specific frequency range of the input signal to suppress ( stopband ) and / or other areas preferentially transmitted; see passband.
Parameters
All the characteristics of a linear filter described by the frequency response or generally by the transfer function.
Transfer functions of filters
Regardless of the specific realization of the filter ( analog or discrete-time or digital) can describe the operation of a filter by its transfer function. This determines how the input signal is modified in amplitude and phase angle.
Transfer functions of analog filters
The filter should be designed in the design based on the desired transfer function. In the choice of the transfer function multipolar analog filter various optimized frequency responses have been proven analog filters depending on the desired filter characteristic:
Transfer functions of digital filters
This primarily applied for analog filter structures transfer functions can be transferred with minor adjustments, even on digital filters in the structure of IIR filters. The adjustments relate this to the essential fact that digital filters with discrete time values and thus a finite base bandwidth work.
Transfer functions non-causal filter
In addition, other transfer functions can be used, which are adapted accordingly depending on the application.
Its transfer function is not causal. They follow a final law, which takes into account not only instantaneous values , but also their history. The transfer function plays an important role due to its simple structure and the model character in the filter theory. The simplest examples are theoretical transfer functions, which practically can not be realized as that of the ideal low-pass filter.
Order
The order of a filter describes the decrease in gain (attenuation and slope ) of frequencies ( far ) above or below the respective cut-off frequency of the filter. It is in low-pass or high-pass filter to the frequency n · approximately 6 dB per octave ( 20 dB per decade · n ), where n represents the order of the filter. For band-pass or band-stop filters, which represent a combination of low-pass and high-pass filters, and thus have two edges of the filter, the filter order as a function of the steepness of the filter edge twice: A bandpass 4th order has 40 dB per decade on.
Higher order filters can be either really created or realized by concatenation of filters of low order ( 1st and 2nd order ).
The transfer function is:
With
Filter types
Filter and frequency response, selection behavior
The theoretical standard cases of the selection behavior of a filter are:
The ideal case of a rectangular or step-like transfer function can be used in practice, however, not reach. As part of the filter for determining the draft of the filter parameters is usually assumed that a normalized low-pass filter. As a result, the determined filter coefficients to be implemented using filter - transformations such as low pass - high pass transform or a low-pass band-pass filter type to the actual transformation of the target system.
Corresponding filter types are both in the low frequency range (eg audio equipment ) and in the high frequency range (eg radio technology ) used.
Parametric filters are in one or more parameters ( frequency, quality ) adjustable and can be operated as a low-pass, high-pass or band-pass filters usually optional. Fields of application are mixing consoles and audio technology.
Linear and non-linear filter
Linear filters
A linear filter with the characteristics of the filtering are independent of signal level. The signal is not distorted. If the input signal increases to a certain frequency by a factor a, the output signal for this frequency is increased accordingly. The shape of the signal is not changed fundamentally. Low pass, high pass, band pass, band-stop and all-pass are referred to as linear filters. But there are also more complex linear filter. For example, an echo effect or a comb filter is also linear.
They can be represented as Vierpolersatzschaltbild.
Nonlinear filter
In a non- linear filter, the characteristics of the filtering depends on the signal level and the time profile of the signal. The signal is distorted in shape. Among the non-linear filters include, for example, limiter, distortion, rectifier (amount), and median filter.
Active vs. passive
Passive filters or electrical filter
The simplest filters based on combinations of resistors ( R), the coil (L), capacitors (C) or, for example, quartz (Q ), or the ceramic elements. Thus, for example filters from RC, RL, LC, LCQ or RCL combinations are possible.
Since these filters can work without external power supply, these combinations ' passive filter ' called. Depending on the structure of the network, the filters act as low-pass, band -pass, high -pass, band stop, or as all-pass filters.
In most filter applications, a sharp transition of the transfer function from the passage - in the stopband is desired. "Sharpness " is indicated by the quality of the filter. The higher the quality, the greater the attenuation in the stopband per decade. The degree and type of transfer function, and thus the number and quality of the components of the filter, as well as the cost of implementation, based on the desired quality.
Passive filters are often referred to by the type of transfer function, such as Bessel, Chebyshev, Cauer filter. They are especially good for filtering tasks in the high frequencies and high power levels, as well as where it comes in all applications on low noise and high linearity.
Active filter or an electronic filter
Active filters are made in addition to the passive components nor of active components such as transistors or operational amplifiers ( op-amp ). This always require active filters its own power supply. In the realization of the active filter in addition to the active components only resistances (R) and capacitors (C) are often used. In this case also, such a filter is called an active RC filter. An active, an analog second-order filter with an operational amplifier and a plurality of resistors and capacitors with particularly simple circuit design is known as a Sallen -Key filter.
With active components inductors can be simulated ( gyrator ), which just at low frequencies (< 1 kHz) can be dispensed with large coils. Active filters have thus the advantage that high grades can be achieved by not using coils.
In addition, the active components allow both easy to integrate amplification of the signal, so that active filters at the same time represent including amplifiers. However, this is not a compelling combination.
Analog filters
A filter is referred to as an analog filter when the time and amplitude signals are processed continuously.
Digital filtering and digital signal processors (DSP)
The digital filters can be classified according to the type of input or output signal; is taken into account, whether they are present analog or digital and continue to be processed. In the first case, the input signal through an A / D converter has to be digitized before it can be processed. After processing, the signal must be implemented by means of a D / A converter again.
By the processing of digitized signals to either signal processors or computers with a degree of flexibility is achieved, which can be achieved by any other filter type. The flexibility is that the filter is modeled by a set of data can be changed relatively easily. So can be implemented with a filter all filter types mentioned above, without hardware changes need to be made.
The often cited as a disadvantage latency, which is caused by the AD and DA conversion, can now be neglected, since it is only a few samples in conventional converters. By using a higher sampling rate (96 kHz), it can be again reduced, since, for example, in DA converter, a low pass filter having a lower slope in favor of a lower latency may be selected.
Digital filters can either edit the signal in the time domain (analogous to other types of filters ) or in the frequency domain.
In the time domain, the advantage of the digital filter is not present in the component tolerances and component aging.
In the frequency domain, the filter can be very flexible, in particular, these filters can be much easier adapted to the existing conditions, since the filter is present as a record.
The transformation between the time domain and the frequency domain ( and vice versa) can be performed, inter alia, of the Fourier or Laplace transform.
Find application in digital filters, for example,
- Audio ( for example, with real time DSP) as an effects device
- Video technology
- Wireless technology
Furthermore, any procedure that reproducibly assigns a digital or analog input signal produces a defined output signal can be understood as a digital filter, such as ciphers or filter functions to audio programs or image editing programs
With digital filters signals can be calculated in real time, except in time independent of their use. For example, it is possible to use very complex machining to restore old recordings.
By folding a beep sound characteristics of complex environments can be imprinted.
See also: FIR filter